Question

It might be predicted that consumer buying behavior would vary with the location of products in a store. Therefore, a team of market researchers looked at the sales per day for a known and unknown brand of candy bars. Additionally, the researchers placed the candy bars in the usual location and next to the cash register in different stores. What can the market researchers conclude with α = 0.01?

known brand		unknown brand
usual	register	usual	register
16 24 19 17 26 30 18	25 15 16 18 31 27 19	11 6 9 13 14 7 11	19 18 16 21 22 17 19

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
Location: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Brand: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Location: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Brand: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a location difference on candy bar sales.There is no location difference on candy bar sales.     

There is a brand difference on candy bar sales.There is no brand difference on candy bar sales.     

There is a location by brand interaction on candy bar sales.There is no location by brand interaction on candy bar sales.     

Answer 1

Anova: Two-Factor With Replication
SUMMARY	usual	register	Total
Known brand
Count	7	7	14
Sum	150	151	301
Average	21.42857	21.57143	21.5
Variance	27.95238	37.28571	30.11538
Unknown brand
Count	7	7	14
Sum	71	132	203
Average	10.14286	18.85714	14.5
Variance	8.809524	4.47619	26.57692
Total
Count	14	14
Sum	221	283
Average	15.78571	20.21429
Variance	51.25824	21.25824
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	343	1	343	17.47241	0.000334	7.822871
Columns	137.2857	1	137.2857	6.993329	0.014197	7.822871
Interaction	128.5714	1	128.5714	6.549424	0.017218	7.822871
Within	471.1429	24	19.63095
Total	1080	27

a) Test statistic used: two-way ANOVA

b)

Location:

critical value = 7.823

test statistic = 6.993

Decision: Fail to reject H0

Brand:

critical value = 7.823

test statistic = 17.472

Decision: Reject H0

Interaction:

critical value = 7.823

test statistic = 6.549

Decision: Fail to reject H0

c)

Location:

η²B = SSB /(SST - SSA - SSAxB) = 137.2857/(1080 - 343 - 128.5714) = 0.2256

small effect

Brand:

η²A = SSA /(SST - SSB - SSAxB) = 343/(1080 - 137.2857 - 128.5714) = 0.4213

medium effect

Interaction:

η²AxB = SSAxB /(SST - SSA - SSB) = 128.5714/(1080 - 343 - 137.2857) = 0.2144

small effect

d) Make an interpretation based on the results.

There is no location difference on candy bar sales.     

There is a brand difference on candy bar sales.

There is no location by brand interaction on candy bar sales.